By rounding each number to 1 significant figure, estimate the value of (612 x 3.9) / 9.8. You must show your rounded values.
(2)
7
The number of grains of sand on a beach is estimated to be 94000000. Write this number in standard form.
(2)
8
Write 0.0000053 in standard form.
(2)
9
Calculate (4 x 103) x (2 x 105). Give your answer in standard form.
(2)
10
Calculate (9 x 106) / (3 x 102). Give your answer in standard form.
(2)
11
Work out (2.4 x 105) + (5 x 104). Give your answer in standard form.
(2)
12
Which of the following correctly represents 3200 in standard form?
A) 32 x 102
B) 3.2 x 103
C) 0.32 x 104
D) 3.2 x 102
13
Write 7.05 x 10-3 as an ordinary number.
(1)
14
Work out (6.1 x 107) - (3.4 x 106). Give your answer in standard form.
(2)
15
A grain of sand has a mass of 3 x 10-5 kg. Calculate the total mass, in kg, of 200000 grains of sand. Give your answer as an ordinary number.
(3)
16
The population of a country is 3.6 x 107. The population of a city within that country is 4.5 x 105. Calculate how many times bigger the population of the country is than the population of the city. Give your answer as an ordinary number.
(3)
17
A company's annual revenue is 2.4 x 108 pounds. Its costs are 1.75 x 108 pounds. Calculate the company's profit, giving your answer in standard form.
(3)
18
A recipe requires ingredients weighed to the nearest gram. Three ingredients weigh 245 g, 128 g and 92 g. By rounding each value to 1 significant figure, estimate the total weight. You must show your rounded values.
(3)
19
The mass of the Earth is approximately 6 x 1024 kg. The mass of the Moon is approximately 7.5 x 1022 kg. Calculate how many times heavier the Earth is than the Moon, giving your answer as an ordinary number.
(3)
20
A field is a rectangle with length 3.5 x 102 metres and width 4 x 101 metres. Calculate the area of the field in square metres, giving your answer in standard form.
(3)
Mark scheme · KS3.M-N3D Number: Standard Form and Rounding: Fluency and Exam Drill
Question 1
B1 6290 cao
Answer: 6290
Question 2
B1 6300 cao
Answer: 6300
Question 3
B1 6000 cao
Answer: 6000
Question 4
B1 2.67 cao
Answer: 2.67
Question 5
M1 identifies the first three significant figures as 3, 8, 2 and the next digit as 6
A1 0.0383 cao
Answer: 0.0383
Question 6
M1 correctly rounds all three values to 1 sf: 600, 4, 10 (oe)
A1 240 cao, from (600 x 4) / 10
Answer: 240
Question 7
M1 coefficient 9.4 identified
A1 9.4 x 107 cao
Answer: 9.4 x 107
Question 8
M1 coefficient 5.3 identified
A1 5.3 x 10-6 cao
Answer: 5.3 x 10-6
Question 9
M1 multiplies coefficients and adds indices: 4 x 2 = 8, 103+5
A1 8 x 108 cao
Answer: 8 x 108
Question 10
M1 divides coefficients and subtracts indices: 9/3 = 3, 106-2
A1 3 x 104 cao
Answer: 3 x 104
Question 11
M1 converts both numbers to the same power of 10 or to ordinary numbers: 240000 and 50000 (oe)
A1 2.9 x 105 cao
Answer: 2.9 x 105
Question 12
B1 selects B
Answer: B (3.2 x 103)
Question 13
B1 0.00705 cao
Answer: 0.00705
Question 14
M1 converts both numbers to the same power of 10 or to ordinary numbers: 61000000 and 3400000 (oe)
A1 5.76 x 107 cao
Answer: 5.76 x 107
Question 15
M1 200000 written as 2 x 105 (oe)
M1 (2 x 105) x (3 x 10-5) = 6 x 100 oe
A1 6 (kg) cao
Answer: 6 kg
Question 16
M1 correct division set up: (3.6 x 107) / (4.5 x 105)
M1 3.6/4.5 = 0.8, index 7-5 = 2, giving 0.8 x 102 oe
A1 80 cao
Answer: 80
Question 17
M1 converts to ordinary numbers or a comparable form: 240000000 and 175000000 (oe)